It's not oxygen, but the air itself that begins the ultimate cure. Aliphatic resin glues are water-thinned as packaged, but waterproof when cured
...Seem to recall that aliphatic resin glues go through a chemical change when or after the water evaporates. That takes time, unless it is accelerated. As mentioned, heat can complete the reaction almost instantaneously. I've used this for years, usually on wing leading edge sheeting, occasionally on capstrips or other thin wood over other structure. Heat penetrates thin wood better.
It's no special thing for a wood-glue bond to be strong enough to tear wood out on either or both sides of the joint. Even Ambroid or SigMent can do that on balsa.
When I use this technique, I wet one surface with aliphatic glue sparingly only along the wood to wood joint. Test fit them, just enough to mark the mating piece very slightly. Redraw a small line of Aliphatic: a small squeeze bottle or syringe with a fine tube like for CyA works. When the glue line has been transferred to the mating piece. Then sparingly renew-rewet the glue line. Wipe that glue off. Only not-quite-dry mating sectors remain at the glue joint .
Assemble the "under and over" pieces - and I emphasize: clamp/block/jig exactly in final alignment. With a Monokote-type iron press, heat through to the joints. Done right, you'll hear a small puff/hiss when [b all[/b] the water is driven out. The joint is then permanent and - apparently- as strong as it would be after a week of room-temperature cure. The only way to realign the glued pieces then involves knives or saws!
OBTW - this can work with thin plywood doublers, but 3/32" may be as thick as you could use, A lot of heat and pressure may be needed over the glue area .